Leah here from leah4sci.com/MCAT and in this video I'm going to show you a trick for how
to raise decimals to an exponent without using a calculator.
On the MCAT you're not allowed to use a calculator but you will be asked to solve mathematical
problems.
Let's say you find yourself with an example .3 squared.
How do you solve this without a calculator and quickly so that it doesn't waste time
on your exam.
If you think about what we're looking at, point three squared means that we have the
number zero point three times zero point three.
This is how you're not going to do it on the MCAT.
This method wastes too much time.
The other way to look at it is to say if we have point three times point three, let's
multiply, three times three, that will give me nine.
And then use the decimal trick.
To make this into a whole number, I have to multiply by ten and multiply by ten.
That means I've just multiplied by ten times ten which is really times a hundred to give
me the answer of nine.
And now I have to undo that by moving the decimal back two spaces dividing by a hundred.
This refers to the decimal trick that I covered earlier in this MCAT Math series for an answer
of point o nine.
This process is a little tedious and this is a relatively simple problem.
As the decimals and the exponents get more complex, you'll need a simpler method because
this would take too long.
So let me show you the shortcut.
We're gonna apply the same method as the last one but in a simpler way so that you rush
through it.
First thing we do is take the exponent on to the number itself.
In this case, we have three squared which gives me nine.
And then we figure out, quickly, how many decimals places we need to move from the right
to the left.
Since we're dealing with numbers less than one, the decimals will be moving to the left.
What you want to do is ask yourself, how many decimals places do I need to move the number
to the right so that I get a whole number.
In this case, point three requires one decimal space to the right to give me a whole number.
That's one space times the number of exponents we have, in this case two, one times two is
two.
That means moving the decimal twice to the right gives me whole numbers so for the answer
I have to move it back twice to the left and that gives me point o'nine.
Notice that this is exactly what we did the long way.
We moved it twice to the right and then unmoved it by moving it twice to the left, but without
actually taking the time to write it all out.
This trick saves you even more time when the numbers are more complex.
For example, if I have point o three squared, let's do the same thing.
We square the number itself, three times three is nine and then count the decimals places.
One, two, two spaces times two for the power so we have two times two, four decimal places
back to the left, one, two, three, four, for an answer that is zero point zero zero zero
nine.
You may wanna put this into scientific notation.
In this case, we have nine times ten to the minus one, two, three, four or if you got
a whole number, just think of it this way; we started with a number nine.
We know that we need to move two decimals places times two to the power which is four.
Isn't moving the decimal back four spaces the same as saying times ten to the minus
four?
That's exactly what we get.
Let's try one more complex example where we'll take the number zero point zero five and raise
it to the third power.
Just to remind you, the long way to solve this problem looks something like this; zero
point o five times zero point o five times zero point o five.
This is going to take way too much time for the MCAT so let's simplify it.
We take the exponent onto the number itself.
In this case, five to the third power is a hundred and twenty five.
How do I know that?
five to the third is five times five times five.
And five times five is twenty five, five times twenty five is one twenty five.
If you don't have this memorized, make sure you download my MCAT Math cheat sheet and
memorize all the equations, all the multiplications, all the decimals, all the fractions.
You have to know them and quickly.
Find this entire series along with the MCAT Math practice quiz and cheat sheet on my website
leah4sci.com./MCATMath.
Now that we have the number one twenty five, let's see what to do about the decimal.
We have to move the decimal space twice to the right to get a whole number, that's two.
The power is three so we multiply by three.
Two times three is six so we have to move the decimal six spaces back that's one, two,
three, four, five, six for an answer that is equal to zero point zero zero zero one
two five.
Again, you probably want to put this into scientific notation which would be one point
two five times ten to the minus one, two, three, four.
While the faster way is to say that we have one twenty five times ten to the minus six
which is what we got when we figured out how many decimal places we need to move back.
But this is not proper scientific notation so we move the decimal back in spaces that's
divide by a hundred and raise this number up to spaces times a hundred, again this is
another trick covered earlier in the series.
And that will give me one point two five times ten to the minus four which we already predicted.
Remember, you are not allowed a calculator on the MCAT and you do not waste precious
times on calculations.
Make sure you go back and study the entire MCAT Math wihout a calculator series and then
try the practice quiz link on my website leah4sci.com/MCATMath.